Use the table to answer the question. House A $124,270 Annual appreciation 4% House B $114,270 Annual appreciation 5% In which o
1 answer:
You might be interested in
Notice that
so the constraint is a set of two lines,
and only the first line passes through the first quadrant.
The distance between any point in the plane is
, but we know that
and
share the same critical points, so we need only worry about minimizing
. The Lagrangian for this problem is then
with partial derivatives (set equal to 0)
We have
which tells us that
so that is a critical point. The Hessian for the target function
is
which is positive definite for all , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is
.